This document discusses scientific notation for writing very large and very small numbers. It explains that scientific notation expresses a number as the product of a number between 1 and 10 and a power of 10. The power of 10 is the exponent that indicates how far the decimal place is moved. Examples are provided of writing numbers in scientific and decimal notation. Rules are given for the format of a number in scientific notation. The document also discusses using negative exponents to write very small numbers in scientific notation. Exercises are provided to practice converting between scientific and decimal notation.
2. Writing Numbers
Scientific notation is used to write
very large and very small numbers.
Today we will focus on only the
larger numbers – using positive
exponents.
The distance to the sun is
150,000,000 km
or 1.5x108 km.
3. Writing in Scientific Notation
In scientific notation, a number is written
m
1 a 10 a 10
using “POWERS OF 10’s”
Let’s investigate using these powers to
understand the pattern.
Do you remember this table from the last
section?
4. Number of zeros = exponent
1 100 1
10 101 10
100 102 10 x 10
1000 103 10 x 10 x10
10,000 104 10x10x10x10
100,000 105 10x10x10x10x10
5. A number in scientific notation has two
parts:
1) a number greater than or equal to 1, but
less than 10
multiplied by
2) A power of ten
6. Moving Places
4x103 = 4x10x10x10 = 4x1000 = 4000
Notice: the exponent on the 10 is 3 and the
decimal after the 4 moved to the right 3
spaces.
2.3x105 = 230,000 moving the decimal right 5
spaces.
2.3x105 is scientific notation and 230,000 is
decimal notation (or standard form).
7. Try these
Write each in scientific notation
1) 320,000,000
2) 45,900
3) 20,000,000,000
4) 38 million
5) 9.22 million
8. Try these
Write each in standard form
1) 8.9 x 105
2) 5 x 104
3) 8.345 x 108
4) 2.9 x 101
5) 5 x 100
9. Explain why these example are NOT in
scientific notation. Be specific!
1) 38.6 x 105
2) 5.2 + 108
3) 10 x 1012
4) 0.4 x 106
10. Part 2 – Small Numbers
Scientific notation can also be used to
represent very, very small numbers.
The DNA in a chromosome is very thin
and tightly packed inside a cell, twisted
and coiled so that it is 1/10000 cm long.
1/10000 = 0.0001
11. Number Decimal Form With Exponents
10 10.0 101
1 1.0 100
1/10 0.1 10-1
1/100 0.01 10 -2
1/1000 0.001 10 -3
12. Remember the rule!
A number in scientific notation has two
parts:
1) a number greater than or equal to 1, but
less than 10
multiplied by
2) A power of ten
13. These numbers today will be small
POSITIVE numbers, but expressed with
negative exponents.
-1 0 1 2
14. Write each number in scientific notation:
1) 0.0035
2) 0.0000006
3) 0.000024
4) 24 millionths
5) 14 thousandths
6) 218 hundred-thousandths
15. Put each in decimal (standard) form:
1) 3.7 x 10 -5
2) 6 x 10 -3
3) 9.752 x 10 -8
4) 1 x 10 -7
